Question

If 5 women or 8 girls can do a work in 84 days. In how many days can 10 women and 5 girls can do the same work?​

Answer 1

Given :

The work done by 5 women or 8 girls = 84 days

To Find :

The number of days in which 10 women and 5 girls can do work

Solution :

∵ The work done by 5 women or 8 girls = 84 days

i.e  5 w = 8 g

Or, 1 w = $\dfrac{8}{5}$ g

∴   10 w = $\dfrac{8}{5}$ g × 10

             = 16 g

∵ The 1's day work for 8 girls = $\dfrac{1}{84}$

The 1's day work for 10 women + 5 girls = $\dfrac{1}{10 w}$ + $\dfrac{1}{5g}$

                                                                  = $\dfrac{1}{16g}$ + $\dfrac{1}{5g}$                ( ∵ 10 w = 16 g)

                                                                  = $\dfrac{21}{80g}$

Now,

∵ 8 girls can complete work in 84 days

Or, 1 girl can complete work in = $\dfrac{84}{8}$

∴ $\dfrac{80}{21}$ girls can complete work in = $\dfrac{84}{8}$  × $\dfrac{80}{21}$   days

                                                    = 4 × 10     days

                                                     = 40 days

Hence, 10 women and 5 girls can do the same work in 40 days . Answer